Mathematics
Grade 11
15 min
Identify functions
Identify functions
What you'll learn
- Identify the number of minutes in an hour and the number of hours in a day with 100% accuracy.
- Solve word problems involving converting between hours and minutes, such as "How many minutes are in 2 hours?", with at least 80% accuracy.
- Explain how to convert a given number of minutes to hours, or hours to minutes, using multiplication or division in their own words.
- Apply their understanding of time units to determine the duration of real-world events, such as calculating how long a movie lasts in minutes given its length in hours and minutes.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a function as a special type of relation with a unique output for each input.
Distinguish between a function and a relation using sets of ordered pairs, mapping diagrams, and tables.
Apply the Vertical Line Test to determine if a graph represents a function.
Algebraically determine if an equation in two variables represents a function of x.
Identify the domain and range of a given relation to support the identification of a function.
Articulate why a given relation is or is not a function, providing specific evidence.
Think of your student ID number. Can one ID number belong to two different students? 🤔 The predictable, one-to-one nature of that relationship is the core idea of a function!
This tutorial will establish the fundamental definition o...
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Key Concepts & Vocabulary
TermDefinitionExample
RelationAny set of ordered pairs, (x, y), which links elements from a set of inputs to a set of outputs.The set R = {(1, 2), (2, 4), (1, 5)} is a relation.
FunctionA special type of relation where every input (x-value) is paired with exactly one output (y-value). No input can have more than one output.The set F = {(1, 2), (2, 4), (3, 6)} is a function because each x-value (1, 2, 3) has only one corresponding y-value.
DomainThe set of all possible input values (the x-coordinates) in a relation.For the relation R = {(1, 2), (2, 4), (1, 5)}, the domain is {1, 2}.
RangeThe set of all possible output values (the y-coordinates) in a relation.For the relation R = {(1, 2), (2, 4), (1, 5)}, the range is {2, 4, 5}.
Mapping DiagramA visual tool that shows how each element of th...
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Core Formulas
The Uniqueness Rule
A relation is a function if for any input x in the domain, there is one and only one output y in the range. If (x, y₁) and (x, y₂) are in the relation, then it must be that y₁ = y₂.
This is the fundamental definition of a function. Use it when analyzing sets of ordered pairs, tables, or mapping diagrams. If you find a single x-value paired with two or more different y-values, the relation is not a function.
The Vertical Line Test
A graph in the Cartesian plane represents a function if and only if no vertical line intersects the graph at more than one point.
This is a graphical method for identifying functions. If you can draw even one vertical line, x = a, that crosses the graph in two or more places, the graph does not represent a function.
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Challenging
A relation is described as 'y is a square root of x'. Is this relation a function for x > 0?
A.Yes, because the principal square root is always used.
B.No, because every positive number x has two square roots, a positive and a negative one.
C.Yes, because the domain is restricted to positive numbers.
D.No, because the range includes negative numbers.
Challenging
Consider the piecewise-defined relation: y = { x + 2, if x < 1; and 2x + 1, if x ≥ 1 }. Is this relation a function?
A.Yes, because the value at the boundary point x=1 is uniquely defined as y=3 by the second piece.
B.No, because at the boundary point x=1, y could be 3 from the first piece or 3 from the second piece.
C.No, because there are two different rules for y.
D.Yes, because both x+2 and 2x+1 are functions on their own.
Challenging
Does the equation x = y⁴ - 2 represent y as a function of x?
A.Yes, because it is a polynomial.
B.No, because y is raised to an even power, leading to two possible y-values for a given x.
C.Yes, because if you solve for y, you get a single expression.
D.No, because the domain is restricted.
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Frequently asked questions
What grade level is "Identify functions"?
Identify functions is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Identify functions?
You'll be able to: Identify the number of minutes in an hour and the number of hours in a day with 100% accuracy; Solve word problems involving converting between hours and minutes, such as "How many minutes are in 2 hours?", with at least 80%….
Is "Identify functions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Identify functions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.